Ashley is 15 years older than Emily. Twelve years ago, Ashley was 4 times as old as Emily. How old is Emily now?
Solution: We can use the given information to write down two equations that describe the ages of Ashley and Emily. Let Ashley's current age be $a$ and Emily's current age be $e$ The information in the first sentence can be expressed in the following equation: $a = e + 15$ Twelve years ago, Ashley was $a - 12$ years old, and Emily was $e - 12$ years old. The information in the second sentence can be expressed in the following equation: $a - 12 = 4(e - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $e$ , it might be easiest to use our first equation for $a$ and substitute it into our second equation. Our first equation is: $a = e + 15$ . Substituting this into our second equation, we get the equation: $(e + 15)$ $-$ $12 = 4(e - 12)$ which combines the information about $e$ from both of our original equations. Simplifying both sides of this equation, we get: $e + 3 = 4 e - 48$ Solving for $e$ , we get: $3 e = 51$ $e = 17$.